Chapter 3 - Section 3.1 - Derivatives of Polynomials and Exponential Functions - 3.1 Exercises - Page 181: 7

$f'\left( t \right) = - 2{e^t}$

$$\eqalign{ & f\left( t \right) = - 2{e^t} \cr & {\text{Differentiate the function}} \cr & f'\left( t \right) = \frac{d}{{dt}}\left[ { - 2{e^t}} \right] \cr & {\text{Use the constant multiple rule}} \cr & f'\left( t \right) = - 2\frac{d}{{dt}}\left[ {{e^t}} \right] \cr & {\text{Apply }}\frac{d}{{dx}}\left[ {{e^x}} \right] = {e^x} \cr & f'\left( t \right) = - 2\left( {{e^t}} \right) \cr & f'\left( t \right) = - 2{e^t} \cr} $$